Spin-dependent transport properties of a single-electron transistor have been analysed, whose two external electrodes and the central part (island) are ferromagnetic. Based on the real-time diagrammatic technique, all transport contributions have been calculated up to the first order in the coupling strength between the island and the leads – this comprises a sequential tunnelling. Relevant occupation probabilities of different charge states are determined from the generalized master equation in the Liouville space. Assuming that spin relaxation processes on the island are sufficiently fast to neglect spin accumulation, we analyze electric current flowing through the system in the parallel and antiparallel magnetic configurations, as well as the resulting tunnel magnetoresistance. We show that transport characteristics of ferromagnetic single-electron transistors exhibit a strong dependence on the magnetic configuration of the system. Furthermore, we also demonstrate that the bias dependence of both the differential conductance and tunnel magnetoresistance displays an oscillatory-like behaviour resulting from single-electron charging effects.